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Shortest and admissible trajectories [1]

Trajectory, a move path of a chess piece, a pawn, a king, a knight or a sliding piece from its origin square to a target square for attack or defense purposes, admissible in n plies, according to a plan. A trajectory of a sliding piece consists of so called alpha-squares, move target squares where the piece is not actually en prise, and empty beta-squares where the piece slides over, and which may be blocked as a defense.

Mathematical Projection

The concept of trajectories with the goal of winning material was formalized by Mikhail Botvinnik in the 60s. Introduced in 1966 at Moscow Central Chess Club [2] , with the skeptical Georgy Adelson-Velsky and others attending, he found Vladimir Butenko as supporter and collaborator, who first implemented the 15x15 vector attacks board representation on a M-20 computer, to determine trajectories. In Botvinnik's hierarchical Mathematical Projection (MP) of chess as a complex system, as apparently implemented in Pioneer, trajectories build the lowest level of the hierarchy. The concepts of zones as intermediate level of the MP consists of a network of main trajectories conform to attacking of defending plans determined elsewhere, negation trajectories, that is opponent's counter trajectories which may block or combat the primary trajectory in time, and own supporting counter-counter trajectories. The MP controls the growth of a search tree inside a best-first search, and prunes all branches forward which could not reach a goal in time.

Linguistic Geometry

Based on the research along with Botvinnik on the project Pioneer, Boris Stilman further formalized the mathematical projection as Linguistic Geometry with the Language of Trajectories, Languages of Trajectory Networks including the Language of Zones, and Languages of Searches including its sub-family, the Languages of Transitions [3].

See also


Forum Posts

External Links


  1. from Boris Stilman (1994). A Linguistic Geometry of the Chess Model. Advances in Computer Chess 7, pdf draft, Figure 3
  2. The last day of the “Botvinnik Memorial” by Anna Burtasova, ChessBase News, September 07, 2011
  3. Boris Stilman (1994). A Linguistic Geometry of the Chess Model. Advances in Computer Chess 7, pdf draft
  4. Paul Rushton, Tony Marsland (1973). Current Chess Programs: A Summary of their Potential and Limitations. INFOR Journal of the Canadian Information Processing Society Vol. 11, No. 1, pdf
  5. Computers, Chess and Long-range Planning by Botvinnik by John L. Jerz
  6. Fovea centralis from Wikipedia
  7. Coq from Wikipedia

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